{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The many faces of the Reverend Bayes: Face 1 Revisited\n",
    "\n",
    "---\n",
    "\n",
    "## ...starting from Face 2 and seeing the  connection...\n",
    "\n",
    "$$\n",
    "\\renewcommand{\\like}{{\\cal L}}\n",
    "\\renewcommand{\\loglike}{{\\ell}}\n",
    "\\renewcommand{\\err}{{\\cal E}}\n",
    "\\renewcommand{\\dat}{{\\cal D}}\n",
    "\\renewcommand{\\hyp}{{\\cal H}}\n",
    "\\renewcommand{\\Ex}[2]{E_{#1}[#2]}\n",
    "\\renewcommand{\\x}{{\\mathbf x}}\n",
    "\\renewcommand{\\v}[1]{{\\mathbf #1}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression in 1D\n",
    "\n",
    "The goal is to fit a straight line: \n",
    "\n",
    "$$ y = ax+b+\\epsilon$$\n",
    "\n",
    "where $\\epsilon \\sim N(0, \\sigma)$\n",
    "and predict $y$ at various $x$'s. \n",
    "\n",
    "Let ${\\bf x} =(x_1, x_2, \\ldots, x_n)$  and\n",
    "$ {\\bf y} =(y_1, y_2, \\ldots, y_n)$ are the actual data. \n",
    "\n",
    "Using Bayesian formalism, we want to estimate the posteriors of the parameter\n",
    "$\\theta =a$ assuming $b=0$. \n",
    "\n",
    "We use  priors $a \\sim N(0, \\sigma_a)$.\n",
    "\n",
    " \n",
    "The implementation below estimates the posterior using Bayes rule  and also samples \n",
    "directly from the product of the likelihood (same as the one in the MLE section above) and prior using the rejection method. \n",
    "\n",
    "Using priors with mean 0 and $\\sigma_a^2=4$. $a \\sim N(0, \\sigma_a)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10930c810>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
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dIKAwHgAAwA0dOHdEs9OSda7wgpn1btxVz/Qar+iwKAub3Z7lXx5Wbn6pYqLD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\nA7M4Spkp7fOXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109238dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## GENERATE SYNTHETIC DATA\n",
    "n=9\n",
    "a = 1.2 # SLOPE\n",
    "b = 0 # INTERSECTION \n",
    "\n",
    "s = 1.5 # STD OF ERROR \n",
    "\n",
    "x = np.random.uniform(low=-3, high=7, size=n) \n",
    "y = a*x+ b + s*np.random.randn(n)\n",
    "\n",
    "\n",
    "#plt.subplot(2,2,2) \n",
    "plt.errorbar(x,y, yerr=s, fmt='o')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "\n",
    "xr = np.linspace(-3, 7, 100) \n",
    "plt.plot(xr, a*xr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the prior and the likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10974d050>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tfDcAdA1KAQBIWr0jV7X1ziUhZ42LU++oEGMDwa/MSItTr8ggSdLerPPKK64w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\nVk8rMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109334910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ======================================\n",
    "## PLOT THE PDF OF THE PRIOR\n",
    "# ======================================\n",
    "I = np.eye(2)\n",
    "\n",
    "## PRIOR \n",
    "sig2 = 4   # WIDTH OF THE PRIOR\n",
    "\n",
    "p_w = lambda (w) : (1/np.sqrt(2*np.pi*sig2))*np.exp( - (w**2)/(2*sig2))\n",
    "\n",
    "asp = np.linspace(-5,5, 100)\n",
    "\n",
    "P=p_w(asp)\n",
    "\n",
    "plt.plot(asp, P)\n",
    "plt.xlabel('slope (a)')\n",
    "plt.title('Prior for a')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the product in the gaussians is taken into the exponential as a sum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Gs8I8PDyaLG885+7u3uw9Adzd3Vus1zQuoy1btrBw4ULGjBnDypUrzWKprq6m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\nESOavCYiIoKsrCyz5mtmZib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EDbpaaNKC87aRBCczKYWdkQQnhA269mOC6+qkxsvDuZXS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\naIIjhBBik2iCI4QQYpP+C07z+KOIqFLOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1095e6fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=1000\n",
    "asp = np.linspace(-1,3, N)\n",
    "\n",
    "p_l = lambda (asp) : (1/np.sqrt(2*np.pi*s**2))*np.exp( - (np.sum( x*x*(y/x-asp)**2)/(2*s**2)))\n",
    "\n",
    "P=np.zeros(N)\n",
    "\n",
    "for k in np.arange(0, asp.size):\n",
    "    P[k] = p_l(asp[k])\n",
    "\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.plot(asp, P)\n",
    "plt.xlabel('slope')\n",
    "plt.ylabel('Likelihood')\n",
    "\n",
    "plt.title('Likelihood');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Sampling for posterior\n",
    "\n",
    "We use a Monte-Carlo method, rejection sampling, to sample from the posterior..we sample a box around it and reject all those samples that dont fall below the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JiYmqrKxUVFSUIiMj3faNjo6W0+n0a7EAAAAAvBPZ8C7/MmTIEF133XV6//33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\nAMEfAAAAMMD/B8pd3VyULCq6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a20d990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=30000\n",
    "asp = np.random.uniform(low=-10, high=10, size=N)\n",
    "\n",
    "\n",
    "\n",
    "post = lambda(wsp): p_l(wsp) * p_w(wsp) \n",
    "\n",
    "ptr = np.zeros(N)\n",
    "\n",
    "for k in np.arange(0, N):\n",
    "    ptr[k]= post(asp[k]) \n",
    "\n",
    "\n",
    "ysp =  np.random.uniform(low=0, high=np.max(ptr), size=N)\n",
    "    \n",
    "idx = (ysp<ptr)\n",
    "\n",
    "\n",
    "g=plt.hist(asp[idx], 20);\n",
    "\n",
    "plt.title('Posterior');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We didnt need to do this here because the posterior is a gaussian, but in real life, most posteriors are not conjugates. And they dont have closed forms. We then need to sample in some fashion. Here we used rejection sampling, but we could equally well use MCMC, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Bayesian formulation of regression and the posterior predictive distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(taken from Am207 class notes)\n",
    "\n",
    "In the linear regression model we have data $D$, of $n$ observations  \n",
    "$D=\\left\\{ ({\\bf x}_1, y_1), ({\\bf x}_2,y_2), \\ldots, ({\\bf x}_n, y_n) \\right\\} $ where ${\\bf x}$ \n",
    "denotes an input vector of dimension $D$ and $y$ denotes a scalar output (dependent variable). \n",
    "All data points are combined into a $D \\times n$ matrix $X$. \n",
    "The model that determines the relationship between inputs and \n",
    "output is given by\n",
    "\n",
    "$$ y   = \\bf x^{T} {\\bf w} + \\epsilon $$\n",
    "\n",
    "where ${\\bf w}$ is a vector of parameters of the linear model. Usually there is \n",
    "a bias or offset is included, but for now we ignore it. \n",
    "\n",
    "We assume that the additive noise  $\\epsilon$ is iid Gaussian with\n",
    "zero mean and variance $\\sigma_n^2$ \n",
    "\n",
    "$$ \\epsilon \\sim N(0, \\sigma^2_n) $$\n",
    "\n",
    "###Likelihood\n",
    "\n",
    "The likelihood is, because we assume independency, the product \n",
    "\n",
    "\\begin{eqnarray} L &=& p(\\bf y|X,\\bf w) = \\prod_{i=1}^{n} p(y_i|\\bf X_i, \\bf w) = \\frac{1}{\\sqrt{2\\pi}\\sigma_n}  \\prod_{i=1}^{n} \n",
    "   \\exp{ \\left( -\\frac{(y_i-\\bf X_i^T \\bf w)^2}{2\\sigma_n^2} \\right)}  \\nonumber \\\\ \n",
    "   &=& \\frac{1}{\\sqrt{2\\pi}\\sigma_n} \\exp{\\left( -\\frac{| \\bf y-X^T \\bf w|^2 }{2\\sigma_n^2} \\right)} = N(X^T \\bf w,  \\sigma_n^2 I)\n",
    "   \\end{eqnarray}\n",
    "   \n",
    "where $|x|$ denotes the Euclidean length of vector $\\bf x$. \n",
    "\n",
    "An alternative way of expressing the likelihood, which is convenient\n",
    "when sampling ${\\bf w}$'s:\n",
    "\n",
    "\\begin{eqnarray} \n",
    "p(\\bf y|\\bf X,\\bf w) &=& \\frac{1}{\\sqrt{2\\pi}\\sigma_n} \\exp{\\left( -\\frac{| X^{-1} \\bf y- \\bf w|^2 \\,\\, (X^{-1} (X^{-1})^{T}) }{2\\sigma_n^2} \\right)} = N(X^{-1} \\bf y,  \\sigma_n^2 (X^{-1} (X^{-1})^{T}) )\n",
    "   \\end{eqnarray}\n",
    "\n",
    "###Prior\n",
    "\n",
    "In the Bayesian framework inference we need to specify a prior\n",
    "over the parameters that expresses our belief about the parameters\n",
    "before we take any measurements. A wise choice is a zero mean \n",
    "Gaussian with covariance matrix $\\Sigma$ \n",
    "\n",
    "\\begin{equation}\n",
    " \\bf w \\sim N(0, \\Sigma) \n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "###Posterior\n",
    "We can now continue with the standard Bayesian formalism \n",
    "\n",
    "\\begin{eqnarray}\n",
    " p(\\bf w| \\bf y,X) &\\propto& p(\\bf y | X, \\bf w) \\, p(\\bf w) \\nonumber \\\\\n",
    "                       &\\propto& \\exp{ \\left(- \\frac{1}{2 \\sigma_n^2}(\\bf y-X^T \\bf w)^T(\\bf y - X^T \\bf w) \\right)}\n",
    "                        \\exp{\\left( -\\frac{1}{2} \\bf w^T \\Sigma^{-1} \\bf w \\right)}  \\nonumber \\\\ \n",
    " \\end{eqnarray}\n",
    " \n",
    "In the next step we `complete the square' and obtain \n",
    "\n",
    "\\begin{equation}\n",
    "p(\\bf w| \\bf y,X)  \\propto  \\exp \\left( -\\frac{1}{2} (\\bf w - \\bar{\\bf w})^T  (\\frac{1}{\\sigma_n^2} X X^T + \\Sigma^{-1})(\\bf w - \\bar{\\bf w} )  \\right)\n",
    "\\end{equation}\n",
    "\n",
    "where $\\bar{\\bf w} = \\sigma_n^{-2}( \\sigma_n^{-2}XX^T +\\Sigma^{-1})^{-1} X \\bf y $\n",
    "\n",
    "This looks like a Gaussian and therefore the posterior is\n",
    "\n",
    "$$ p(\\bf w| X, {\\bf y}) \\sim {\\cal N}( \\frac{1}{\\sigma_n^2} A^{-1}Xy , A^{-1} ) $$ \n",
    "\n",
    "where $A= \\sigma_n^{-2}XX^T +\\Sigma^{-1}$\n",
    "\n",
    "To make predictions for a test case we average over all possible parameter predictive distribution\n",
    "values, weighted by their posterior probability. This is in contrast to non Bayesian schemes, where a single parameter is typically chosen by some criterion. \n",
    "\n",
    "###Regularization\n",
    "\n",
    "If we assume that $\\Sigma$ is a diagonal covariance matrix so that\n",
    "\n",
    "$$\\bf w \\sim N(0, \\alpha \\bf I)$$\n",
    "\n",
    "then we get back alpha as the regularization parameter from ridge regression, since our \"estimation risk\" is just the log of the gaussian, and terms in exponents add!!\n",
    "\n",
    "Similarly Lasso comes from a laplace prior.\n",
    "\n",
    "###Posterior Predictive Distribution\n",
    "\n",
    "Thus the predictive distribution at some $x^{*}$ is given by averaging the output of all possible linear models w.r.t. the  posterior\n",
    "\n",
    "\\begin{eqnarray} \n",
    "p(y^{*} | x^{*}, {\\bf x,y}) &=& \\int p({\\bf y}^{*}| {\\bf x}^{*}, {\\bf w} ) p(\\bf w| X, y)dw \\nonumber \\\\\n",
    "                                    &=& {\\cal N} \\left(\\frac{1}{\\sigma_n^2} x^{*^{T}} A^{-1} X {\\bf y}, x^{*^T}A^{-1}x^{*} \\right),\n",
    "\\end{eqnarray}\n",
    "\n",
    "which is again Gaussian, with a mean given by the posterior mean multiplied by the test input\n",
    "and the variance is a quadratic\n",
    "form of the test input with the posterior covariance matrix, showing that the\n",
    "predictive uncertainties grow with the magnitude of the test input, as one would\n",
    "expect for a linear model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10a445510>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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1dJ8NzvYrAECJWADGpEqlkhUrFjd7GgDQ0tyGBAAAFIkFAACgSCwAAABFYgEAACgSCwAA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\nAEViAQAAKPr/zv0ZvxM1SsYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3a5a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a0=-0.3\n",
    "a1=0.5\n",
    "N=20\n",
    "noiseSD=0.2\n",
    "priorPrecision=2.0\n",
    "u=np.random.rand(20)\n",
    "x=2.*u -1.\n",
    "def randnms(mu, sigma, n):\n",
    "    return sigma*np.random.randn(n) + mu\n",
    "y=a0+a1*x+randnms(0.,noiseSD,N)\n",
    "plt.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import multivariate_normal\n",
    "def cplot(f, ax=None):\n",
    "    if not ax:\n",
    "        plt.figure()\n",
    "        ax=plt.gca()\n",
    "    xx,yy=np.mgrid[-1:1:.01,-1:1:.01]\n",
    "    pos = np.empty(xx.shape + (2,))\n",
    "    pos[:, :, 0] = xx\n",
    "    pos[:, :, 1] = yy\n",
    "    ax.contourf(xx, yy, f(pos))\n",
    "    #data = [x, y]\n",
    "    return ax\n",
    "def plotSampleLines(mu, sigma, numberOfLines, dataPoints=None, ax=None):\n",
    "    #Plot the specified number of lines of the form y = w0 + w1*x in [-1,1]x[-1,1] by\n",
    "    # drawing w0, w1 from a bivariate normal distribution with specified values\n",
    "    # for mu = mean and sigma = covariance Matrix. Also plot the data points as\n",
    "    # blue circles. \n",
    "    #print \"datap\",dataPoints\n",
    "    if not ax:\n",
    "        plt.figure()\n",
    "        ax=plt.gca()\n",
    "    for i in range(numberOfLines):\n",
    "        w = np.random.multivariate_normal(mu,sigma)\n",
    "        func = lambda x: w[0] + w[1]*x\n",
    "        xx=np.array([-1,1])\n",
    "        ax.plot(xx,func(xx),'r', alpha=0.5)\n",
    "    if dataPoints:\n",
    "        ax.scatter(dataPoints[0],dataPoints[1])\n",
    "    ax.set_xlim([-1,1])\n",
    "    ax.set_ylim([-1,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0021447551423913074"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihoodSD = noiseSD # Assume the likelihood precision, beta, is known.\n",
    "likelihoodPrecision = 1./(likelihoodSD*likelihoodSD)\n",
    "priorMean = np.zeros(2)\n",
    "priorSigma = np.eye(2)/priorPrecision #Covariance Matrix\n",
    "priorPDF = lambda w: multivariate_normal.pdf(w,priorMean,priorSigma)\n",
    "priorPDF([1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+8Y913XXX6ZprrtHevXv1wAMP6Nvf/ramTcu8SQAAAACayOUTg6+66ir97d/+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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10972c3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cplot(priorPDF);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hc8OtxETrcbs/JyXxYxQyZK5KSoCvfIV3ZxsaWL4BACMjwLvvctb8pk3A5s3a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\nUGChYfduC0W+gu3jx+106bVrpcmT3Z4tMCwIC9HCcWyrUM+6gitXAu/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HYyuOeXnSqVP2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\n7mgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a699b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotSampleLines(priorMean,priorSigma,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Given the mean = priorMu and covarianceMatrix = priorSigma of a prior\n",
    "# Gaussian distribution over regression parameters; observed data, xtrain\n",
    "# and ytrain; and the likelihood precision, generate the posterior\n",
    "# distribution, postW via Bayesian updating and return the updated values\n",
    "# for mu and sigma. xtrain is a design matrix whose first column is the all\n",
    "# ones vector.\n",
    "def update(x,y,likelihoodPrecision,priorMu,priorSigma): \n",
    "    postSigmaInv  = np.linalg.inv(priorSigma) + likelihoodPrecision*np.outer(x.T,x)\n",
    "    postSigma = np.linalg.inv(postSigmaInv)\n",
    "    postMu = np.dot(np.dot(postSigma,np.linalg.inv(priorSigma)),priorMu) + likelihoodPrecision*np.dot(postSigma,np.outer(x.T,y)).flatten()\n",
    "    postW = lambda w: multivariate_normal.pdf(w,postMu,postSigma)\n",
    "    return postW,postMu,postSigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NDvBVEYBCufqt8LQCPtiNAavfROS28HCZguFpVfy//5tV8WCTmAjcfjtwxx1q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29OdJPdgqKjo2EymVBVVdXsZxUVFVZfb349IiJyD06aEHlZebkE7zt35LhLF+Dpp1uerVYVFkqp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\nTURERESkkP8B32l4MjfSCpMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aed5ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For each iteration plot  the\n",
    "# posterior over the first i data points and sample lines whose\n",
    "# parameters are drawn from the corresponding posterior. \n",
    "fig, axes=plt.subplots(figsize=(12,30), nrows=5, ncols=2);\n",
    "mu = priorMean\n",
    "sigma = priorSigma\n",
    "iterations=2\n",
    "muhash={}\n",
    "sigmahash={}\n",
    "k=0\n",
    "for i in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]:\n",
    "    postW,mu,sigma = update(np.array([1,x[i]]),y[i],likelihoodPrecision,mu,sigma)\n",
    "    muhash[i]=mu\n",
    "    sigmahash[i]=sigma\n",
    "    if i in [1,4,7,10,19]:\n",
    "        cplot(postW, axes[k][0])\n",
    "        plotSampleLines(muhash[i],sigmahash[i],6, (x[0:i],y[0:i]), axes[k][1])\n",
    "        k=k+1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The multiple risks\n",
    "\n",
    "We learned earlier that there are *two risks in learning* that we must consider, one to *estimate probabilities*, which we call **estimation risk**, and one to *make decisions*, which we call **decision risk**. We motivated these by the different processes needed to estimate probabilities and make decisions, but deferred a further discussion of them. Now's the time to have that discussion.\n",
    "\n",
    "What do we mean by a \"decision\" exactly? We'll use the letter $g$ here to indicate a decision, in both the regression and classification problems. In the classification problem, one example of a decision is the process used to choose the class of a sample, given the probability of being in that class. As another example, consider the cancer story from before. The decision may be: ought we biopsy, or ought we not biopsy. By minimizing the estimation risk, we obtain a probability that the patient has cancer. We must mix these probabilities with \"business knowledge\" or \"domain knowledge\" to make a decision. \n",
    "\n",
    "What we must additionally supply is the **decision loss** $l(y,g)$ or **utility** $u(l,g)$ (profit, or benefit) in making a decision $g$ when the predicted variable has value $y$. For example, we must provide all of the losses $l$(no-cancer, biopsy), $l$(cancer, biopsy), $l$(no-cancer, no-biopsy), and $l$(cancer, no-biopsy). One set of choices for these losses may be 20, 0, 0, 200 respectively.\n",
    "\n",
    "To simplify matters though, lets presently insist that the **decision space** from which the decision $g$is chosen is the same as the space from which $y$ is chosen. In other words, the decision to be made is a classification. Then we can use these losses to penalize mis-classification asymmetrically if we desire. In the cancer example, we then set $l$(observed-no-cancer, predicted cancer) to be 20 and $l$(observed-cancer, predicted-no-cancer) to be 200. This is the situation we encountered before where we penalize the false negative(observed cancer not predicted to be cancer) much more than the false positive(observed non-cancer predicted to be cancer)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circling the wagons: Learning uses average risk\n",
    "\n",
    "What is this process? The idea is quite simple, and you have probably already thought about it intuitively even without knowing it. We simply weigh each combinations loss by the probability that that combination can happen:\n",
    "\n",
    "$$R_{g}(x) = \\sum_y l(y,g(x)) p(y|x).$$\n",
    "\n",
    "That is, we calculate the **average risk** over all choices y, of making choice g for a given sample.\n",
    "\n",
    "Then, if we want to calculate the overall risk, given all the samples in our set, we calculate:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "R(g) &=& \\sum_x p(x) R_{g}(x) = \\sum_x p(x) \\sum_y l(y,g(x)) p(y|x) \\\\\n",
    "&=& \\sum_x \\sum_y l(y,g(x)) p(x) p(y|x) = \\sum_x \\sum_y l(y,g(x)) p(x,y)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "To make the best decision, we then minimize over all possible decisions $g(x)$:\n",
    "\n",
    "$$g^* = \\arg\\min_{g} R(g).$$\n",
    "\n",
    "for which it is enough to do the minimization on a per-sample basis:\n",
    "\n",
    "$$g^*(x) = \\arg\\min_{g(x) \\in y} R_{g}(x).$$\n",
    "\n",
    "For example, if there are two classes $1$ and $0$ we can classify data into, we have:\n",
    "\n",
    "$$R_g(x) = l(1, g)p(1|x) + l(0, g)p(0|x).$$\n",
    "\n",
    "Then for the \"decision\" $g=1$ we have:\n",
    "\n",
    "$$R_1(x) = l(1,1)p(1|x) + l(0,1)p(0|x),$$\n",
    "\n",
    "and for the \"decision\" $g=0$ we have:\n",
    "\n",
    "$$R_0(x) = l(1,0)p(1|x) + l(0,0)p(0|x).$$\n",
    "\n",
    "Now, we'd choose $1$ for the sample at $x$ if:\n",
    "\n",
    "$$R_1(x) \\le R_0(x).$$\n",
    "\n",
    "This process is illustrated in the diagram below."
   ]
  },
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   "source": [
    "####The symmetric case with 1-0 risk\n",
    "\n",
    "For the 1-0 loss, $l(1,1) = l(0,0) =0$ and $l(1,0) = l(0,1) = 1$, and we get:\n",
    "\n",
    "$$R_1(x) = p(0|x), R_0(x) = p(1|x).$$\n",
    "\n",
    "We'd choose $1$ if:\n",
    "\n",
    "$$R_1(x) \\le R_0(x)$$\n",
    "\n",
    "for a given sample $x$. Thus we get back the \"intuitive\" prescrription for classification we have been using so far: **choose $1$ if**:\n",
    "\n",
    "$$p(1|x) \\ge p(0|x).$$\n",
    "\n",
    "Since these add to 1, this is equivalent to saying **choose $1$ if $p(1|x) \\ge 0.5$**\n",
    "\n",
    "This risk is one you cant do better than, and is called the **Bayes Risk**."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where in the machine learning process ought one to do this risk penalization? Remember again that there are two risks in learning. The first risk is the estimation risk, and we use this to *estimate the model on the training set*. We then cross-validate by calculating a score, or risk, on the validation set, and minimizing it. What is this risk that we minimize on the validation set? Is this the estimation risk, or is this the decision risk?\n",
    "\n",
    "Remember that ERM is actually a special case of the risk minimization rule introduced here. Lets see this again (wee saw it before in Bayes 1). Basically we choose as the joint probability $p(x, y)$ a special kind of function which has the value $1/N$ at every sample and zero elsewhere: this is called the **empirical probability distribution** and is written like this:\n",
    "\n",
    "$$p(x,y) = \\frac{1}{N}\\sum_{i \\in \\dat} \\delta(x - x_i) \\delta(y - y_i).$$\n",
    "\n",
    "The function $\\delta(x - x_i)$ is a very simple function, called the **Dirac Delta** function, which has value 1 at $x=x_i$ and 0 elsewhere. Thus\n",
    "\n",
    "$$\\sum_x f(x) \\delta(x - x_i) = f(x_i)$$\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "R(g) = \\sum_x \\sum_y l(y,g(x)) p(x,y) &=& \\sum_x \\sum_y l(y, g(x)) \\frac{1}{N}\\sum_{i \\in \\dat} \\delta(x - x_i) \\delta(y - y_i)\\\\\n",
    "&=& \\frac{1}{N}\\sum_{i \\in \\dat} \\left(\\sum_x \\delta(x - x_i) \\sum_y  \\delta(y - y_i) l(y, g(x)) \\right)\\\\\n",
    "&=& \\frac{1}{N}\\sum_{i \\in \\dat} \\left(\\sum_x \\delta(x - x_i) l(y_i, g(x)) \\right)\\\\\n",
    "&=& \\frac{1}{N}\\sum_{i \\in \\dat} l(y_i, g(x_i))\n",
    "\\end{eqnarray*}\n",
    "\n",
    "Models like SVM which do not give us probabilities are learned directly with the ERM risk both as estimation and decision risk. "
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###The regression case\n",
    "\n",
    "####The use of the posterior predictive\n",
    "\n",
    "This is exactly the risk we use in ERM. For regression we use $l(y_i, g(x_i)) = (y_i - g(x_i)^2$, where we interpret $g$ to be a **point-estimate** from a distribution of possible $y$'s at a given x. Where did this distribution arise from? In the Bayesian scenario this distribution arises naturally as the *posterior predictive*. In the frequentist scenario, we get them from different samples of our true population. Well, each set gives us a different $y$ and thus we get a distribution at a given x. Now, whow do we choose g? We can use decision loss $l(y,g) = (g-y)^2$ or even $l(y,g) = | g- y |$. The former one leads to the mean as the point estimate, the latter the median. \n",
    "\n",
    "This is why in beginning stats courses, the regression line is $E[y|x]$. It didnt have to be, but the choice of the squared loss makes it so.\n",
    "\n",
    "Remember that the idea we used in empirical risk minimization (ERM) is that validation or cross-validation risk is a proxy that estimates the risk on the population, the out-of-sample risk. But, notice from above that ERM minimizes decision risk, having **already estimated the probability distribution by the empirical probability distribution**. Thus, the model with the lowest cross-validation risk minimizes the population or out of sample error, leading to a model which generalizes well in the sense that the model that **will best minimize decision risk on future samples**. Or to put it another way, minimize the decision risk in your c-val process. Thats why standard `sklearn` uses accuracy, and cross-validation routines allow us to specify different scores, such as the F1-score, etc. And this is why you should be calculating ROC curves on the validation set, rather than the test set as we did on the homework. (The other reason for doing that is that it gives us an inference on the ROC curve, AUC, or associated metric)."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Back to classification\n",
    "\n",
    "Typically, in a probabilistic classification model, say for example, when we do logistic regression with a log-loss, we have used this log-loss as an estimation loss to obtain the probability density $p(y|x)$. Two things now need to happen in the validation process: (a) we need to estimate the regularization parameter $C$, and (b) we need to make classification decisions using our decision risk.\n",
    "\n",
    "####Setting the hyperparameters\n",
    "But remember that we also set hyperparameters like $C$ based on our validation process. At first glance, this might seem wierd, since the regularization term is part of the estimation loss. But if you think about *choosing hyperparameters as choosing between different models, as opposed to choosing parameters of a model*, the wierdness goes away. What you do is you choose a value of $C$ on the grid, and *then train* the models other parameters using *estimation risk* on the training data. We then calculate the *decision risk* on the validation data. We compare all these decision risks and choose the $C$ with the lowest decision risk; that is, we choose the *model* with the smallest validation-set decision risk:\n",
    "\n",
    "$$R_{decision}(g_C) = \\frac{1}{N} \\sum_{i \\in \\dat_{validation}} l(y_i,g_C(x_i)).$$\n",
    "\n",
    "$$g_{C^*} = \\arg\\min_{g_C} R_{decision}(g_C).$$\n",
    "\n",
    "Here $g_C$ indicates that the model is chosen for a particular value of $C$, and $C^*$ is the final value we settle on as part of the minimization process.If our decision loss is different, such as in the asymmetric case, it is this asymmetric loss we must use at the validation stage, since *generalization means finding a model that will best minimize decision risk on future samples*. \n",
    "\n",
    "Note that validation sets are typically smaller than training sets, since we are fitting less hyperparameters like $C$ in this model selection process on the validation set than model parameters like logistic regression coefficients on the training sets.\n",
    "\n",
    "####Validation is ERM on decision risk\n",
    "\n",
    "Something else might be bothering you now. When we trained our model on the training set for a given value of $C$, we did two things: we estimated the parameters of the model, and we estimated $p(y|x)$. Why not use this probability directly in the equation for overall risk to calculate it? Why are we doing the sum over validation points above? The answer is that we dont have an estimate of $p(x)$, which is needed in the calculation of the overall risk. So instead we must use an approximation to $p(x)$:\n",
    "\n",
    "$$p(x) = \\frac{1}{N_{validation}} \\sum_{i \\in \\dat_{validation}} \\delta(x - x_i)$$\n",
    "\n",
    "which then gives us the equation we used above.\n",
    "\n",
    "####Recap of the process of learning\n",
    "\n",
    "With these loose ends tied up, lets recap what we did: we used the estimation loss (log-loss in Logistic Regression) to estimate the probabilities. Then we were faced with the problem of converting the probabilities into classification decisions. For this we used the decision loss on the validation data set, which might be identical to the estimation loss, a 1-0 loss in the symmetric case, or even an asymmetric loss like the one used above. The validation process provides a second service: model selection, helping us pick the best validation parameter. Furthermore, the validation risk is  an unbiased estimate of the out-of-sample risk, and by using the decision risk as the validation risk, we ensure that \"good generalization\" means choosing a model which makes the \"right\" decisions on future data.\n",
    "\n",
    "In ERM only models like SVM (where we use a regularized hinge loss), there is no probability estimation. Typically we'lll use the same loss for parameter estimation (rather than likelihood or probability estimation) in the estimation phase on the training data, as we use in the decision phase on the validation data. Of-course if we directly want to make a decision like biopsy|no-biopsy or an asymmetric classification, we alter the decision risk to take care of this, having trained the parameters of our model (such as the SVM line/plane coefficients)."
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